Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:

from bisect import bisect_left

def index(a, x):
    # 'Locate the leftmost value exactly equal to x'
    i = bisect_left(a, x)
    if i != len(a) and a[i] == x:
        return True
    return -1
c = int(input())
list1 = []

for i in range(50000):

    z = ((i)*(i+1))//2

    list1.append(z)
# print(list1)
temp = 0
for i in list1:
    z = c - i
    k = index(list1,z)
    if k == True and z!=c and c!=i:
        # print(z,i)
        temp = 1
        break

if temp == 0:
    print('NO')
else:
    print('YES')